On transverse invariants from Khovanov homology

Abstract

O. Plamenevskaya associated to each transverse knot K an element of the Khovanov homology of K. In this paper, we give two refinements of Plamenevskaya's invariant, one valued in Bar-Natan's deformation of the Khovanov complex and another as a cohomotopy element of the Khovanov spectrum. We show that the first of these refinements is invariant under negative flypes and SZ moves; this implies that Plamenevskaya's class is also invariant under these moves. We go on to show that for small-crossing transverse knots K, both refinements are determined by the classical invariants of K.

32 pages. V2: updated to accepted version

References in corpus (4)

• A Khovanov stable homotopy type
• Combinatorial knot contact homology and transverse knots
• Heegaard Floer invariants of Legendrian knots in contact three--manifolds
• Legendrian and transverse cables of positive torus knots

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